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Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation

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Date
2005
Dewey
Probabilités et Mathématiques appliquées
Sujet
Mathematical Physics; Physics
Journal issue
Communications in Mathematical Physics
Volume
257
Number
3
Publication date
2005
Article pages
515-562
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00220-005-1343-4
URI
https://basepub.dauphine.fr/handle/123456789/1016
Collections
  • CEREMADE : Publications
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Author
Séré, Eric
Lewin, Mathieu
Hainzl, Christian
Type
Article accepté pour publication ou publié
Abstract (EN)
According to Diracrsquos ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator D0. In the presence of an external field, these virtual particles react and the vacuum becomes polarized. In this paper, following Chaix and Iracane (J. Phys. B 22, 3791–3814 (1989)), we consider the Bogoliubov-Dirac-Fock model, which is derived from no-photon QED. The corresponding BDF-energy takes the polarization of the vacuum into account and is bounded from below. A BDF-stable vacuum is defined to be a minimizer of this energy. If it exists, such a minimizer is the solution of a self-consistent equation. We show the existence of a unique minimizer of the BDF-energy in the presence of an external electrostatic field, by means of a fixed-point approach. This minimizer is interpreted as the polarized vacuum.

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